But Odriozola has aimed to play down that speculation, insisting he is happy to continue at the Basque club.
"I renewed my contract with La Real until 2022 for a reason," Odriozola told Diario AS.
"When you are playing with the Spain your future is magnified [by the media] but the only thing in my head is Real Sociedad, nothing else matters.
"I only ever try to do my job and perform well, not to think about anything else including transfers or how I performed with Spain.
"Now my time with the national team is over and I'm now fully focused on La Real.
"Everything has happened very quickly and you simply don't have time to look back, only to the here and now."
Odriozola has made nine appearances for Sociedad in all competitions this term.